Abstract
This article deals with prime ideals in Ore extensions S=Rα[X] over the right Noetherian K-algebra R. More specifically, we try to determine the structure of the centre $$Z( \mathcal{Q}(S/P))$$ of the classical ring of quotients of S modulo a prime ideal P from corresponding data in R. The main result asserts that $$Z(\mathcal{Q}(S/P))$$ is always a finitely generated field extension of K, provided this holds for the prime ideals in R. This yields a somewhat more elementary proof of a result in [6] which states that for any prime P in the group algebra R=K[G] of a polycyclic-by-finite group G, $$Z( \mathcal{Q}(S/P))$$ is a finitely generated field extension of K.
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